1. Field of the Invention
The present invention relates to reconstruction of sampled signals. More particularly, the invention relates to a method and apparatus for compressed sensing that utilizes a combined compressed sensing matrix to at least partially reconstruct an input signal.
2. Description of the Related Art
Sampling is a method of converting an analog signal into a numeric sequence. Analog signals are often sampled at spaced time intervals to form digital representations for storage, analysis, processing, or other uses. Typically an analog signal must be sampled at or above its Nyquist rate, which may be defined as twice the bandwidth of the analog signal or twice the highest frequency component of the analog signal in the case of baseband sampling. For wide bandwidth signals, sampling at the Nyquist rate requires a great amount of computing resources, processing power, and data storage. Furthermore, if the sampled data is to be transmitted to a secondary location, a large amount of bandwidth is required as well.
It is known, however, that if the signal to be sampled is sparse or compressible, i.e. there is a relatively small amount of data contained within limited components of the signal (expressed in time domain, frequency domain, and/or other transform domain), then sampling at the Nyquist rate is an inefficient use of resources. In the case of sparse or compressible signals, a recently developed method of sampling known as compressed sensing provides a theoretical basis for sampling at less than the Nyquist rate with either no or minimal information loss so that the compressed samples may be reconstructed as an accurate full-bandwidth representation or estimate of the original signals.
Unfortunately, known compressed sensing methods suffer from several limitations. For example, most physically realizable compressed sensing methods rely either on narrowband frequency sampling or random time sampling. Sampling only with narrowband frequency filters results in poor performance for signals with sparse representation in the frequency domain and sampling only with random time sampling results in poor performance for signals with a sparse representation in the time domain. Further, known compressed sensing methods have not been reduced to practice for effective physical implementation.